You are what you eat (diet) and where you eat (trophic level) in the food web. The relative abundance of pairs of stable isotopes of the organic elements carbon (e.g., the isotope ratio of <sup>13</sup>C v...You are what you eat (diet) and where you eat (trophic level) in the food web. The relative abundance of pairs of stable isotopes of the organic elements carbon (e.g., the isotope ratio of <sup>13</sup>C vs<sup> 12</sup>C), nitrogen, and sulfur, among others, in the tissues of a consumer reflects a weighted-average of the isotope ratios in the sources it consumes, after some corrections for the processes of digestion and assimilation. We extended a Bayesian mixing model to infer trophic positions of consumer organisms in a food web in addition to the degree to which distinct resource pools (diet sources) support consumers. The novel features in this work include: 1) trophic level estimation (vertical position in foodweb) and 2) the Bayesian exposition of a biologically realistic model [1] including stable isotope ratios and concentrations of carbon, nitrogen, and sulfur, isotopic fractionations, elemental assimilation efficiencies, as well as extensive use of prior information. We discuss issues of parameter identifiability in the complex and most realistic model. We apply our model to simulated data and to bottlenose dolphins (Tursiops truncatus) feeding on several numerically abundant fish species, which in turn feed on other fish and primary producing plants and algae present in St. George Sound, FL, USA. Finally, we discuss extensions from other work that apply to this model and three important general ecological applications. Online supplementary materials include data, OpenBUGS scripts, and simulation details.展开更多
The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation t...The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation to information are developed here. The Arrow-Pratt absolute risk aversion measure is shown to be related to the Cramer-Rao Information bound. The derivative of the log-likelihood function is seen to provide a measure of information related stability for the Bayesian posterior density. As well, information similar prior densities can be defined reflecting the central role of likelihood in the Bayes learning paradigm.展开更多
文摘You are what you eat (diet) and where you eat (trophic level) in the food web. The relative abundance of pairs of stable isotopes of the organic elements carbon (e.g., the isotope ratio of <sup>13</sup>C vs<sup> 12</sup>C), nitrogen, and sulfur, among others, in the tissues of a consumer reflects a weighted-average of the isotope ratios in the sources it consumes, after some corrections for the processes of digestion and assimilation. We extended a Bayesian mixing model to infer trophic positions of consumer organisms in a food web in addition to the degree to which distinct resource pools (diet sources) support consumers. The novel features in this work include: 1) trophic level estimation (vertical position in foodweb) and 2) the Bayesian exposition of a biologically realistic model [1] including stable isotope ratios and concentrations of carbon, nitrogen, and sulfur, isotopic fractionations, elemental assimilation efficiencies, as well as extensive use of prior information. We discuss issues of parameter identifiability in the complex and most realistic model. We apply our model to simulated data and to bottlenose dolphins (Tursiops truncatus) feeding on several numerically abundant fish species, which in turn feed on other fish and primary producing plants and algae present in St. George Sound, FL, USA. Finally, we discuss extensions from other work that apply to this model and three important general ecological applications. Online supplementary materials include data, OpenBUGS scripts, and simulation details.
文摘The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation to information are developed here. The Arrow-Pratt absolute risk aversion measure is shown to be related to the Cramer-Rao Information bound. The derivative of the log-likelihood function is seen to provide a measure of information related stability for the Bayesian posterior density. As well, information similar prior densities can be defined reflecting the central role of likelihood in the Bayes learning paradigm.
